Conservation of mass and energy

The model equations are determined by writing the balance equations based on the conservation of mass and energy. Tlie balance equations have the following basic form ... 

The first law is one of conservation of mass and energy, whereby a balance exists between energy, work, and heat quantities. The second law relates to energy flow, whereby heat can only flow from a hotter body to a colder one. 

Consider any region of space that has a hnite volume and prescribed boundaries that unambiguously separate the region from the rest of the universe. Such a region is called a control volume, and the laws of conservation of mass and energy may be applied to it. We ignore nuclear processes so that there are separate conservation laws for mass and energy. For mass. 

Whitwell, J. C. and Toner, R. K. Conservation of Mass and Energy (McGraw-Hill, 1969). 

Vessel blowdown. The previously mentioned relationships for the critical flow rate of a steam-water mixture can be employed with the conservation of mass and energy for a vessel of fixed volume to determine its time-dependent blowdown properties. The range of problems associated with coolant decompression in water-cooled reactors is quite broad. The types of hypothetical (some are even incredible) reactor accidents may be... 

The basic principle used to calculate the temperature in a compartment fire is the conservation of mass and energy. Since the energy release rate and the compartment temperature change with time, the application of the conservation laws will lead to a series of differential equations. 

To control, optimize, or evaluate the behavior of a chemical plant, it is important to know its current status. This is determined by the values of the process variables contained in the model chosen to represent the operation of the plant. This model is constituted, in general, by the equations of conservation of mass and energy. 

A first principle mathematical description of a CSTR is based on balance equations expressing the general laws of conservation of mass and energy. Assuming that n components are mixed, the material balance of the i-component, taking into account all forms of supply and discharge in the volume V of the... 

The condition satisfied whenever the total energy of any closed system is constant. Thus, for a chemical reaction there is no loss or gain of energy in a closed system however, energy may be transformed from one form into another. See Conservation of Mass and Energy Thermodynamics... 

Process models allow composite case manufacturers to determine the affects of process variable settings on final cylinder quality. Because the cost of a composite cylinder can be as great as 500,000, the ability to simulate filament winding can significantly reduce cost and improve quality. Several computer models of the filament-winding process for both thermoset and thermoplastic matrix materials have been developed. These models are based on engineering principles such as conservation of mass and energy. As such, numerous resin systems and fiber materials can be modeled. 

A particular chemical reaction may be written to embody both laws of conservation of mass and energy as demonstrated below ... 

To begin, we select a control volume around the entire cell and consider the transient thermal behavior via a conservation of mass and energy. The calculated outputs from the model will be the SOFC temperature versus time. Figure 9.7 shows a schematic of the problem to be analyzed. 

In order to make design or operation decisions a process engineer uses a process model. A process model is a set of mathematical equations that allows one to predict the behavior of a chemical process system. Mathematical models can be fundamental, empirical, or (more often) a combination of the two. Fundamental models are based on known physical-chemical relationships, such as the conservation of mass and energy, as well as thermodynamic (phase equilibria, etc.) and transport phenomena and reaction kinetics. An empirical model is often a simple regression of dependent variables as a function of independent variables. In this section, we focus on the development of process models, while Section III focuses on their numerical solution. 

There being two components and two phases in the following streams at the bottom, feed and overhead, Gibbs s law states that only two of the three variables (pressure, temperature, and composition) are independent. Therefore, the number of independent variables is only 11. The number of defining equations is two (the conservation of mass and energy), and, therefore, the number of degrees of freedom for this process is 11 - 2 = 9. Consequently, not more than nine automatic controllers can be placed on this process. 

Wei, Russell, and Swartzlander The Structure of the Chemical Processing Industries Whitwell and Toner Conservation of Mass and Energy... 

From Eq. (7.186), conservation of mass and energy, and the chemical potential, the rate of change of entropy per unit volume is obtained as... 

Positron decay occurs in proton-rich nuclei. In this case, the positron (or p+ particle) is originated by conversion of a proton into a neutron, along with the emission of a neutrino to conserve the energy. Positrons are the antiparticle of electrons. In a very fast process (10 12s), emitted positrons collide with an electron of a nearby atom and both particles disappear in a process called annihilation. The necessary conservation of mass and energy accounts for the transformation of the mass of both particles into energy, which is characteristically emitted in the form of two 511-keV photons almost in opposite directions. Consequently, positron emitters are used to label radiopharmaceuticals produced with diagnostic purposes by imaging. 

The conservation of mass and energy for a textile material give the following equations ... 

In this section we derive the equation of motion that governs the natural convection flow in laminar boundary layer. The conservation of mass and energy equations derived in Chapter 6 for forced convection are also applicable for natural convection, but tlie momentum equation needs to be modified to incorporate buoyancy. 

A dynamic one-dimensional model of char gasification in a fixed-bed reactor has been developed. The model is based on conservation of mass and energy together with chemical equilibrium in the gas phase between H2O, H2, CO2, CO, using the water-gas shift reaction. Methane is assumed inactive in the char bed. The basic equations are ... 

Rudd, D. F., Powers, G. J., and Siirola, J. J. (1973) Process Synthesis (Prentice-Hall). Whitwell, J. C. and Toner, R. K. (1969) Conservation of Mass and Energy (McGraw-Hill). Williams, E. T. and Jackson, R. C. (1958) Stoichiometry for Chemical Engineers (McGraw-Hill). 

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